Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system

Details Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system Cohomological study on variants of the Mumford system, and integrability of the Noumi-Yamada system

2005-01-18

arxiv.org/abs/math-ph/0501048v3

Physics

Mathematical Physics

22 pages, an extensively revised version

Scientific paper

10.1007/s00220-006-0028-y

The purpose of this paper is twofold. The first is to apply the method introduced in the works of Nakayashiki and Smirnov on the Mumford system to its variants. The other is to establish a relation between the Mumford system and the isospectral limit $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$ of the Noumi-Yamada system. As a consequence, we prove the algebraically completely integrability of the systems $\mathcal{Q}_g^{(I)}$ and $\mathcal{Q}_g^{(II)}$, and get explicit descriptions of their solutions.

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